Minimal Active Space: NOSCF and NOSI in Multistate Density Functional Theory

17 October 2022, Version 2
This content is a preprint and has not undergone peer review at the time of posting.


In this Perspective, we introduce a minimal active space (MAS) for the lowest N eigenstates of a molecular system in the framework of a multistate density functional theory (MSDFT), consisting of no more than N2 nonorthgonal Slater determinants. In comparison with some methods in wave function theory in which one seeks to expand the ever increasing size of an active space to approximate the wave functions, it is possible to have an upper bound in MSDFT because the auxiliary states in a MAS are used to represent the exact N-dimensional matrix density D(r). In analogy to Kohn-Sham DFT, we partition the total Hamiltonian matrix functional H[D] into an orbital-dependent part, including multistate kinetic energy and Coulomb-exchange energy plus an external potential energy, and a correlation matrix density functional Ec[D]. The latter accounts for the part of correlation energy not explicitly included in the minimal active space. However, a major difference from Kohn-Sham DFT is that state interactions are necessary to represent the N-matrix density D(r) in MSDFT, rather than a non-interacting reference state for the scalar ground-state density. Two computational approaches are highlighted. We first derive a set of non-orthogonal multistate self-consistent-field (NOSCF) equations for the variational optimization of H[D]. We introduce the multistate correlation potential, as the functional derivative of Ec[D], which includes both correlation effects within the MAS and that from the correlation matrix functional. Alternatively, we describe a non-orthogonal state interaction (NOSI) procedure, in which the determinant functions are optimized separately. Both computational methods are useful for determining the exact eigenstate energies and for constructing variational diabatic states, provided that the universal correlation matrix functional is known. It is hoped that this discussion would stimulate developments of approximate multistate density functionals both for the ground and excited states.


Multi-State Density Functional Theory
Non-orthogonal Self-Consistent-Field Theory
Conical Intersection
Spin Interaction
Quantum Chemistry


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.